Unit 6 Lesson 1 The Pythagorean Theorem

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Presentation transcript:

Unit 6 Lesson 1 The Pythagorean Theorem CCSS Lesson Goals G-SRT 4: Prove theorems about triangles. Use the Pythagorean Th. to find missing side lengths in a right triangle. Recognize a Pythagorean Triple. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

the Pythagorean Theorem In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. c a b

proof Given Perpendicular Post. Right D Altitude Th B e D c a f A C b Statement Reason Given Perpendicular Post. Right D Altitude Th Def similar polygons Cross-Products Prop. Add. Prop. of = Distributive Prop Segment Add. Post Substitution

definition A set of three positive integers: a, b, c Pythagorean Triples A set of three positive integers: a, b, c that satisfy the equation Examples 3, 4, and 5 5, 12, and 13 8, 15, and 17

example Find the missing side B a A C 12 Do the side lengths form a Pythagorean Triple?

You Try Find the missing side B c 7 A 24 C Do the side lengths form a Pythagorean Triple?

You Try Find the missing side Do the side lengths form a Pythagorean Triple?

example Find the area of the triangle.

You Try Find the area of the triangle

example Two antennas are each supported by 100 foot cables. If the cables are attached to the antennas 50 feet from the ground, how far apart are the antennas? d 50 ft 100 ft 100 ft 50 ft x

summary How is the Pythagorean Theorem useful? What is the difference between the Pythagorean Theorem in general and a Pythagorean Triple?

Today’s Assignment p. 538: 8, 14, 18 – 28 e, 31 – 33, 37

Find the unknown side length. Simplify answers that are radicals Find the unknown side length. Simplify answers that are radicals. Tell whether the side lengths form a Pythagorean triple. Find the area of the figure. Round decimal answers to the nearest tenth. Find the value of x. Simplify answers that are radicals. The variables r and s represent the lengths of the legs of a right triangle, and t represents the length of the hypotenuse. The values of r, s, and t form a Pythagorean triple. Find the unknown value.